Historical note:

Einstein, Bohr, De Broglie, and Heisenberg all looked for a cause for the strange results they discovered

Schrödinger developed his equation from data that was collected. This is like Newton's universal gravity, Newton was able to predict the behavior of the planets in our solar system, but never was able to explain why. It took 200 years of scientific advancements for Einstein was able to explain gravity (Sort of). Will it take that long for an explanation of why Schrödinger's equation works, maybe, if it is ever explained.